Question #056a7

1 Answer
Nov 5, 2017

sec^2(x)

Explanation:

Rewrite the expression: 1+tanx=1+sinx/cosx

=d/dx (1+sinx/cosx)

differentiate the sum term by term

= d/dx(1)+d/dx(sinx/cosx)

the derivative of 1 is zero

d/dx(sinx/cosx)

Use the quitient rule

(d/dx((sinx))cosx-(d/dx(cosx)sinx))/(cos^(x))

simplify

(cos^2(x)+sin^2(x))/(cos^2(x)

use the Pythagorean identity cos^2(x)+sin^2(x)=1

=(1/cos^2(x))

=sec^2(x)